Marnus Labuschagne and Xavier Bartlett put on a century stand to steer Australia to 187-8 in 42 overs after they slumped to 0-3 against Bangladesh in the rain-hit second ODI on Thursday.
Bangladesh will chase a revised target of 192 from 41 overs, after rain interrupted play in Dhaka to end Australia's innings prematurely in the 50-overs match.
Labuschagne remained unbeaten on 55 after Bartlett hit 52 off 48 balls as the pair combined to rescue the visitors out of a historic early collapse.
Australia lost three batters for ducks inside two overs in what became only the fourth instance in ODI history of a team losing three wickets without scoring.
Taskin Ahmed removed Matthew Short for the second time in as many matches in the series, the opener shouldering arms to an in-swinger that came back sharply to uproot his stumps.
Mustafizur Rahman then struck twice in the second over, drawing outside edges from left-handers Cooper Connolly and Matt Renshaw.
Alex Carey, the left-handed wicketkeeper-batter was caught at point off Mustafizur for 13.
Skipper Josh Inglis, who made 34, and Cameron Green, who scored 25, fell to left-arm spinner Tanvir Islam and Australia slumped further at 81-6.
Labuschagne and Bartlett then combined to lift Australia in a 103-run seventh-wicket stand before Taskin returned for his third spell to break the partnership, dismissing Bartlett.
Taskin bowled Adam Zampa on the next ball before Nathan Ellis survived the hat-trick.
Rain then halted play for nearly three hours.
Taskin and Mustafizur finished with three wickets each. Tanvir claimed two.
Bangladesh, who lead the three-match series 1-0, are eying their first-ever ODI series win over Australia.